Discovering Abstract Algebra
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Author | : John K. Osoinach, Jr. |
Publisher | : American Mathematical Soc. |
Total Pages | : 199 |
Release | : 2021-10-04 |
Genre | : Education |
ISBN | : 147046442X |
Discovering Abstract Algebra takes an Inquiry-Based Learning approach to the subject, leading students to discover for themselves its main themes and techniques. Concepts are introduced conversationally through extensive examples and student investigation before being formally defined. Students will develop skills in carefully making statements and writing proofs, while they simultaneously build a sense of ownership over the ideas and results. The book has been extensively tested and reinforced at points of common student misunderstanding or confusion, and includes a wealth of exercises at a variety of levels. The contents were deliberately organized to follow the recommendations of the MAA's 2015 Curriculum Guide. The book is ideal for a one- or two-semester course in abstract algebra, and will prepare students well for graduate-level study in algebra.
Author | : Charles C Pinter |
Publisher | : Courier Corporation |
Total Pages | : 402 |
Release | : 2010-01-14 |
Genre | : Mathematics |
ISBN | : 0486474178 |
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Author | : Thomas Judson |
Publisher | : Orthogonal Publishing L3c |
Total Pages | : 0 |
Release | : 2023-08-11 |
Genre | : |
ISBN | : 9781944325190 |
Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.
Author | : Steven J. Rosenberg |
Publisher | : CRC Press |
Total Pages | : 397 |
Release | : 2021-12-22 |
Genre | : Mathematics |
ISBN | : 1000516334 |
Studying abstract algebra can be an adventure of awe-inspiring discovery. The subject need not be watered down nor should it be presented as if all students will become mathematics instructors. This is a beautiful, profound, and useful field which is part of the shared language of many areas both within and outside of mathematics. To begin this journey of discovery, some experience with mathematical reasoning is beneficial. This text takes a fairly rigorous approach to its subject, and expects the reader to understand and create proofs as well as examples throughout. The book follows a single arc, starting from humble beginnings with arithmetic and high-school algebra, gradually introducing abstract structures and concepts, and culminating with Niels Henrik Abel and Evariste Galois’ achievement in understanding how we can—and cannot—represent the roots of polynomials. The mathematically experienced reader may recognize a bias toward commutative algebra and fondness for number theory. The presentation includes the following features: Exercises are designed to support and extend the material in the chapter, as well as prepare for the succeeding chapters. The text can be used for a one, two, or three-term course. Each new topic is motivated with a question. A collection of projects appears in Chapter 23. Abstract algebra is indeed a deep subject; it can transform not only the way one thinks about mathematics, but the way that one thinks—period. This book is offered as a manual to a new way of thinking. The author’s aim is to instill the desire to understand the material, to encourage more discovery, and to develop an appreciation of the subject for its own sake.
Author | : Wieb Bosma |
Publisher | : Springer Science & Business Media |
Total Pages | : 387 |
Release | : 2007-07-10 |
Genre | : Computers |
ISBN | : 3540376348 |
Based on the ontology and semantics of algebra, the computer algebra system Magma enables users to rapidly formulate and perform calculations in abstract parts of mathematics. Edited by the principal designers of the program, this book explores Magma. Coverage ranges from number theory and algebraic geometry, through representation theory and group theory to discrete mathematics and graph theory. Includes case studies describing computations underpinning new theoretical results.
Author | : Stephen Lovett |
Publisher | : CRC Press |
Total Pages | : 717 |
Release | : 2015-07-13 |
Genre | : Mathematics |
ISBN | : 1482248913 |
A Discovery-Based Approach to Learning about Algebraic StructuresAbstract Algebra: Structures and Applications helps students understand the abstraction of modern algebra. It emphasizes the more general concept of an algebraic structure while simultaneously covering applications. The text can be used in a variety of courses, from a one-semester int
Author | : John Edward Maxfield |
Publisher | : Courier Corporation |
Total Pages | : 228 |
Release | : 2010-03-01 |
Genre | : Mathematics |
ISBN | : 0486477231 |
The American Mathematical Monthly recommended this advanced undergraduate-level text for teacher education. It starts with groups, rings, fields, and polynomials and advances to Galois theory, radicals and roots of unity, and solution by radicals. Numerous examples, illustrations, commentaries, and exercises enhance the text, along with 13 appendices. 1971 edition.
Author | : Tony Barnard |
Publisher | : CRC Press |
Total Pages | : 286 |
Release | : 2016-12-19 |
Genre | : Mathematics |
ISBN | : 1315405768 |
Discovering Group Theory: A Transition to Advanced Mathematics presents the usual material that is found in a first course on groups and then does a bit more. The book is intended for students who find the kind of reasoning in abstract mathematics courses unfamiliar and need extra support in this transition to advanced mathematics. The book gives a number of examples of groups and subgroups, including permutation groups, dihedral groups, and groups of integer residue classes. The book goes on to study cosets and finishes with the first isomorphism theorem. Very little is assumed as background knowledge on the part of the reader. Some facility in algebraic manipulation is required, and a working knowledge of some of the properties of integers, such as knowing how to factorize integers into prime factors. The book aims to help students with the transition from concrete to abstract mathematical thinking.
Author | : John W. Lawrence |
Publisher | : Cambridge University Press |
Total Pages | : 640 |
Release | : 2021-04-15 |
Genre | : Mathematics |
ISBN | : 1108865518 |
Through this book, upper undergraduate mathematics majors will master a challenging yet rewarding subject, and approach advanced studies in algebra, number theory and geometry with confidence. Groups, rings and fields are covered in depth with a strong emphasis on irreducible polynomials, a fresh approach to modules and linear algebra, a fresh take on Gröbner theory, and a group theoretic treatment of Rejewski's deciphering of the Enigma machine. It includes a detailed treatment of the basics on finite groups, including Sylow theory and the structure of finite abelian groups. Galois theory and its applications to polynomial equations and geometric constructions are treated in depth. Those interested in computations will appreciate the novel treatment of division algorithms. This rigorous text 'gets to the point', focusing on concisely demonstrating the concept at hand, taking a 'definitions first, examples next' approach. Exercises reinforce the main ideas of the text and encourage students' creativity.
Author | : Stephen Boyd |
Publisher | : Cambridge University Press |
Total Pages | : 477 |
Release | : 2018-06-07 |
Genre | : Business & Economics |
ISBN | : 1316518965 |
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.